Should VARCHAR columns be put at the end of table definitions in MySQL?

I've heard (from a colleague, who heard it from another developer) that VARCHAR columns should always be put at the end of a table definition in MySQL, because they are variable in length and could therefore slow down queries.

The research I've done on stack overflow seems to contradict this however and suggests that column order is important, while there is varying agreement on how much this applies to VARCHARs.

He wasn't specific about storage engines, or about whether this only applied to VARCHAR columns which are infrequently accessed.